I quickly looked through my files on animal diseases -
these files are small as the topic is of very limited interest -
and did not find anything on cancer in wild chimps. I do
have parts of articles on atherosclerosis in wild elephants (and
primates - it seems baboons are the best studied primate
in this regard), pneumonia in bighorn mountain sheep,
tuberculosis in wild deer in India, viral and bacterial
diseases in marine mammals [I believe cancer is found in
marine mammals but did not photocopy that section of the
subject reference. If my memory is correct, the reference I have
parts of, had some unpleasant photos of dolphins with large tumors and
cancers.] Also: encephalitis in multiple animal species,
conjunctivitis in birds, etc.

If one is willing to spend some time in a good research library,
I suspect you might find published evidence of cancer in at least some
wild animals.  Until the references are cited, those in denial may prevail.

Two good references here are:

JOURNAL OF WILDLIFE DISEASES
WILDLIFE DISEASE NEWSLETTER

Those who deny that wild animals get sick, should spend some
time reviewing back issues of the above in a good research
library. It makes for interesting reading!

Tom Billings